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We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magnetohydrodynamic (MHD) flows. Numerical simulations were performed with up to $1024^3$ collocation…
The diffusion and flow of amorphous materials, such as glasses and granular materials, has resisted a simple microscopic description, analogous to defect theories for crystals. Early models were based on either gas-like inelastic collisions…
We study the dynamics of a granular gas heated by the stochastic thermostat. From a Boltzmann description, we derive the hydrodynamic equations for small perturbations around the stationary state that is reached in the long time limit.…
We study interactions between shocks and standing-wave patterns in vertically oscillated layers of granular media using three-dimensional, time-dependent numerical solutions of continuum equations to Navier-Stokes order. We simulate a layer…
Fluidisation is the process by which the weight of a bed of particles is supported by a gas flow passing through it from below. When fluidised materials flow down an incline, the dynamics of the motion differ from their non-fluidised…
Here we investigate the Cauchy problem for the inhomogeneous Navier-Stokes equations in the whole $n$-dimensional space. Under some smallness assumption on the data, we show the existence of global-in-time unique solutions in a critical…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…
The existence of weak solutions to the Navier-Stokes-Fourier system describing the stationary states of a compressible, viscous, and heat conducting fluid in bounded 2D-domains is shown under fairly general and physically relevant…
Based on experiments of the compaction of granular materials under periodic shear of a packing of glass beads, a minimal model for the dynamics of the packing density as a function of time is proposed. First, a random ``energy landscape''…
We present a numerical simulation of a granular material using hydrodynamic equations. We show that, in the absence of external forces, such a system phase-separates into high density and low density regions. We show that this separation is…
The decay of turbulent and laminar oblique bands in the lower transitional range of plane Couette flow is studied by means of direct numerical simulations of the Navier--Stokes equations. We consider systems that are extended enough for…
We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…
A coarse-grained particle model for incompressible Navier-Stokes (NS) equation is proposed based on spatial filtering by utilizing smoothed particle hydrodynamics (SPH) approximations. This model is similar to our previous developed SPH…
An oxidation process is simulated for a bundle of metal tubes in a cross-flow. A fluid flow is governed by the incompressible Navier-Stokes equations. To describe the transport of oxygen, the corresponding convection-diffusion equation is…
A dynamic procedure for the Lagrangian Averaged Navier-Stokes-$\alpha$ (LANS-$\alpha$) equations is developed where the variation in the parameter $\alpha$ in the direction of anisotropy is determined in a self-consistent way from data…
In this paper, we give an overview of the results established in [3] which provides the first rigorous derivation of hydrodynamic equations from the Boltzmann equation for inelastic hard spheres in 3D. In particular, we obtain a new system…
Efficient assessment of convolved hidden Markov models is discussed. The bottom-layer is defined as an unobservable categorical first-order Markov chain, while the middle-layer is assumed to be a Gaussian spatial variable conditional on the…
A two-dimensional lattice model for the formation and evolution of shear bands in granular media is proposed. Each lattice site is assigned a random variable which reflects the local density. At every time step, the strain is localized…
The Navier-Stokes systems for compressible fluids with density-dependent viscosities are considered in the present paper. These equations, in particular, include the ones which are rigorously derived recently as the Saint-Venant system for…
Hamiltonian particle systems may exhibit non-linear hydrodynamic phenomena as the time evolution of the density fields of energy, momentum, and mass. In this Letter, an exact equation describing the time evolution is derived assuming the…